Sighed is not really appropriate as a tag verb, even though some people may treat it as one. Dictionary.com does give a definition as a transitive verb, but I find it nonsensical to vocalize a sentence into a sigh.

Therefore, I am treating as a beat rather than a tag. As a beat, it goes in the same paragraph as the dialog element, but as a separate sentence. A tag also goes in the same paragraph, but is part of the sentence containing the quote fragment:

The officer asked, "Is that all?"

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This should make it clearer, with a verb that cannot reasonably be mistaken for a tag:

Sighed is not really appropriate as a tag verb, even though some people may treat it as one. Dictionary.com does give a definition as a transitive verb, but I find it nonsensical to vocalize a sentence into a sigh.

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I think it's transitive because of constructions like "He sighed a heavy sigh." I agree that it doesn't work at all well as a tag for a speech act. (To be honest, I don't think it works well in "He sighed a heavy sigh" either, because it sounds cliched, but at least it makes sense there.)

The officer sighed, "Is that all?"
or
The officer sighed.
"Is that all?"

I'm pretty sure it's the first one, just posting here for confirmation.

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I've been reading far more than writing the past while and have seen it done both ways. That, of course, means very little. My own perference is the former, I think it ties the action to the comments, and is, therefore, easier for me to follow. However the latter may have it's place in creating suspense or what have you.